Hydraulic actuator with a frequency dependent relative pressure ratio

ABSTRACT

Disclosed herein are hydraulic actuators and methods for the operation of actuators having variable relative pressure ratios. Further disclosed are methods for designing and/or operating a hydraulic actuator such that the actuator exhibits a variable relative pressure ratio. In certain embodiments, the relative pressure ratio of the hydraulic actuator may be dependent on one or more characteristics (such as, for example, frequency or rate of change) of an oscillating input to the hydraulic actuator.

CROSS REFERENCE OF RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.17/089,137, filed Nov. 4, 2020, which is a continuation of U.S.application Ser. No. 16/484,967, filed Aug. 9, 2019, which is a nationalstage filing under 35 U.S.C. 371 of International Patent ApplicationSerial No. PCT/US2018/017879, filed Feb. 12, 2018, which claims thebenefit of priority under 35 U.S.C. § 119(e) of U.S. ProvisionalApplication No. 62/457,933, filed Feb. 12, 2017, the disclosures of eachof which are incorporated herein by reference in their entirety.

BACKGROUND

During the last forty years, a number of automotive manufacturers haveattempted to utilize hydraulic actuators in automobiles. However,hydraulic-based active suspension systems have yet to achieve widespreadadoption and commercial success in the automotive field.

SUMMARY

Inventors have recognized that there is often a tradeoff between a forcecapability of a hydraulic actuator and a response time of the hydraulicactuator. This trade-off may hinder the use of hydraulic actuators inapplications in which both high force capability and fast response timesare desired. Various methods, systems, and apparatuses are describedherein to at least partially overcome this disadvantage.

In one aspect, a hydraulic actuator is disclosed that comprises: ahydraulic cylinder that includes an extension chamber and a compressionchamber; a hydraulic pump, with a first port and a second port, capableof generating, or configured to generate, a pressure differentialbetween the compression chamber the extension chamber. In certainembodiments, the hydraulic actuator further includes a first gas chargedaccumulator; a second gas charged accumulator; a first fluid flow pathfluidically connecting the first port to the first gas chargedaccumulator; a second fluid flow path fluidically connecting the firstport to the extension chamber; a third fluid flow path fluidicallyconnecting the second port to the second gas charged accumulator; and afourth fluid flow path fluidically connecting the second port to thecompression chamber. The hydraulic cylinder may also include a housingat least partially enclosing an internal volume containing a quantity ofhydraulic fluid, a piston slidably received in the housing, therebydividing the internal volume into a compression chamber and an extensionchamber, and a piston rod attached to the piston. In certain embodimentsat least a portion of the first flow path and a portion of the secondflow path are the same and at least a portion of the third flow path andthe fourth flow path are the same.

In certain embodiments, the hydraulic actuator exhibits a first relativecompliance factor when exposed to a first oscillating input, and asecond relative compliance factor when exposed to a second oscillatinginput, wherein: the frequency of the first oscillating input is lessthan the frequency of the second oscillating input, and the firstrelative compliance factor is greater than the second relativecompliance factor. Alternatively or additionally, the hydraulic actuatormay exhibit a first relative pressure factor in response to a firstoscillating input, and a second relative pressure factor in response toa second oscillating input, and wherein: the frequency of the firstoscillating input is below the frequency of the second oscillatinginput; and the first relative pressure factor is less than the secondrelative pressure factor. In various embodiments, the frequency of thefirst oscillating input may be between 0-3 Hz exclusive and thefrequency of the second oscillating input may be between 5-20 Hzexclusive. First and second oscillating inputs in other frequency rangesincluding those that are larger or smaller than the ranges indicatedabove are contemplated as the disclosure is not so limited.

In certain embodiments a restriction element or hydraulic control devicemay be arranged along the first flow path. In certain embodiments, therestriction element is configured to vary an impedance or inertance ofthe first flow path, or a portion thereof, based at least in part on afrequency of an input (e.g., a frequency of an oscillating torqueapplied to the pump, a frequency of an oscillating force exerted on thepiston rod) relative to the impedance or inertance of a second flowpath. In various exemplary embodiments, this restriction element may bea shim stack, a passive restriction, an orifice, a variable orificevalve, or an actively controlled valve. In certain embodiments, therestriction element includes an actively controlled valve, and thehydraulic actuator further includes a controller configured to actuate(e.g., at least partially open or at least partially close) the activelycontrolled valve based at least in part on a frequency of an input.

In another aspect, a vehicle is disclosed having a suspension systemthat, in various embodiments, includes at least one, at least two, atleast three, or at least four hydraulic actuators according to any ofthe embodiments disclosed herein. In certain embodiments, the vehiclemay have a plurality of wheels, and each wheel of the vehicle may beassociated with a respective hydraulic actuator. In certain embodiments,the vehicle may include at least one hydraulic actuator, or a portionthereof, that is disposed between an unsprung mass of the vehicle and asprung mass of the vehicle.

It should be appreciated that the foregoing concepts, and additionalconcepts discussed below, may be arranged in any suitable combination,as the present disclosure is not limited in this respect. It isenvisioned that any feature of any embodiment may be combined with anyother feature of any other embodiment. Further, other advantages andnovel features of the present disclosure will become apparent from thefollowing detailed description of various non-limiting embodiments whenconsidered in conjunction with the accompanying figures. Further, itshould be understood that the various features illustrated or describedin connection with the different exemplary embodiments described hereinmay be combined with features of other embodiments or aspects. Suchcombinations are intended to be included within the scope of the presentdisclosure.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an embodiment of a hydraulic actuator with acompression side accumulator.

FIG. 2 illustrates an embodiment of a hydraulic actuator with anextension side accumulator.

FIG. 3 illustrates an embodiment of a hydraulic actuator with acompression side and an extension side accumulator.

FIG. 4 illustrates the hydraulic actuator of FIG. 3 with a restrictionelement in the path of the extension side accumulator.

FIG. 5 demonstrates an example of the frequency dependence of therelative pressure factor for a hydraulic actuator.

FIG. 6 illustrates an embodiment of a hydraulic actuator with acompression side accumulator and two extension side accumulators.

FIG. 7 demonstrates increase in the force produced by an embodiment ofthe hydraulic actuator illustrated in FIG. 4.

FIG. 8 demonstrates a plot of relative motion ratio as a function ofinput frequency.

FIG. 9 demonstrates a plot of damping rate as a function of inputfrequency

FIG. 10 illustrates an embodiment with multiple hydraulic actuators witha shared extension chamber compliance element.

DETAILED DESCRIPTION

Inventors have realized that there is often a trade-off between forcecapability of an actuator and the response time of an actuator. Theapparatus and methods described herein at least partially overcome thisdisadvantage of actuator systems for applications where high force andfast response time are desired. In one embodiment, an actuator isdisclosed that has increased force capability for low speed events, anddecreased force capability but faster response times for high speedevents. It is contemplated that such an actuator may find application inan active suspension system of a vehicle, in which both high forcecapability and fast response times are desirable.

Turning now to the figures, several non-limiting embodiments aredescribed in detail. FIG. 1 illustrates an exemplary suspension systemincluding a hydraulic actuator 30. The illustrated hydraulic actuatorincludes a hydraulic cylinder with a piston 32 slidably received in atleast a portion of the hydraulic cylinder. The actuator illustrated inFIG. 1 also includes a compression chamber 33 partially defined by afirst face 32 a of the piston 32, an extension chamber 34 partiallydefined by a second face 32 b of the piston, and a piston rod 35attached to the second face of the piston. The illustrated hydraulicactuator further comprises a pump 31, a compression-side flow path 36 athat allows for fluid exchange between the compression chamber 34 andport 31 a of the pump 31, and an extension-side flow path 36 b thatallows for fluid flow from the extension chamber to the pump. Notably,the illustrated actuator embodiment includes only a single accumulator 7located on the compression-side of the actuator, i.e. is in fluidcommunication with compression volume 33. In certain embodiments, thepump may be configured to function as both a hydraulic pump in an activemode and as a hydraulic motor in a regenerative mode. In certainembodiments, the pump may be replaced with a hydraulic motor configuredto function as both a hydraulic pump in an active mode and as ahydraulic motor in a regenerative mode.

As described in more detail herein, pressure generated by the pump or ahydraulic motor, being used as a pump, may act on the piston to produceactive forces and/or resistive forces on the piston. An active force onthe piston is a net hydraulic force that acts on the piston in thedirection of motion of the piston. A resistive force is a net hydraulicforce that acts on the piston opposite to the direction of motion of thepiston. The accumulator 7 may be in fluid communication with thecompression volume, and may serve to accept the volume of fluiddisplaced by the rod when the rod penetrates further into the damperbody.

FIG. 2 illustrates an alternative embodiment of a suspension system,wherein the hydraulic actuator comprises only a single accumulator 7 a 1located on the extension-side of the actuator. FIG. 3 illustrates yetanother alternative embodiment, in which the hydraulic actuator 40includes two accumulators: a compression side-accumulator 52 in fluidcommunication with the compression chamber and/or an extension-sideaccumulator 51 in fluid communication with the extension chamber (e.g.,fluidically connected to the extension-side flow path). In an exemplaryapplication, the hydraulic actuator of any of FIGS. 1-3 may beinterposed between a wheel assembly 41 of a vehicle (unsprung mass) andthe body 42 of the vehicle (sprung mass), and may be arranged inparallel with a spring element 43 (e.g. a coil spring or an air spring).

The inventors have recognized that the number of accumulators and theirfluidic placement, and in systems comprising more than one accumulators,the relative sizes of each accumulator, may substantially affect theoverall behavior of the actuator. The following discussion illustrateshow various pressures within different chambers of the actuator, and howoutput force produced by the actuator, are affected by placement andrelative sizes of accumulators in the system. Inventors have realizedthat the size of the accumulator is indicative of the amount of gas andnot simply the size of the accumulator housing. The gas volumeestablishes compliance of the accumulator and helps determine thecompliance of a portion and/or the entire hydraulic system. However,other compliance elements or means for controlling compliance besidesgas filled accumulators (e.g. accumulators with spring loaded pistons,compressible hydraulic fluids, flexible housings and hydraulic hoseswith flexible walls) may be used as the disclosure is not so limited.

In the embodiment illustrated in FIG. 3, the actuator includes anhydraulic cylinder 54 with a piston 56 slidably received in at least aportion of the hydraulic cylinder with a compression chamber 57partially defined by a first face 56 a of the piston 56, and anextension chamber 58 partially defined by a second face 56 b of thepiston. The illustrated hydraulic actuator further includes a pump 55, acompression-side flow path 59 a that allows for fluid flow between thecompression chamber 57 and the pump 55, an extension-side flow path 59 bthat allows for fluid flow between the extension chamber 58 and the pump55, a compression-side accumulator 52, and an extension-side accumulator51.

When a torque is applied to the pump (or to a hydraulic motor beingoperated as a pump), the hydraulic device may generate a pressuredifferential, denoted ΔP_(pump), between the fluidic pressure in theextension chamber (denoted Pext) and fluidic pressure in the compressionchamber (denoted Pcom).

ΔP _(pump) =P _(ext) −P _(com)  Equation 1

The pressure differential generated by the pump may be related to thetorque applied to the pump via equation 2:

$\begin{matrix}{{\Delta P_{pump}} = {E\frac{\left( {\tau_{applied} - {J\overset{.}{\omega}} - \tau_{drag}} \right)}{Disp}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where τ_(applied) is the applied torque, J is the moment of inertia ofthe pump, τ_(drag) represents drag torque, E represents an efficiencyfactor (e.g., to account for mechanical efficiency of the pump and/orpressure drops associated with various flow paths), and Disp is thedisplacement volume of the pump. For a low-inertia pump operating underlow drag conditions and assuming mechanical efficiency of 1, equation 2may be reduced such that equation 2 may be used to acceptablyapproximate the pressure differential ΔP_(pump) generated as a result ofa given applied torque.

$\begin{matrix}{{\Delta P_{pump}} = \frac{\tau_{applied}}{Disp}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

For example, if a torque of +10 N·m is applied to a pump having adisplacement of 2 cubic meters, a pressure differential of approximately5 Pa will be generated by the pump. As indicated above, other parameters(e.g., additional efficiency factors, conversion factors for units,etc.), depending on specific pump and system design, may also affect thepressure differential generated by the applied torque.

Utilizing equation 3 (which assumes a mechanical efficiency of 1 andneglects inertia and drag) with exemplary displacement value of 2 cubicmeters and an applied torque of +10 N·m, a pressure differential of +5Pa may be generated by the pump (e.g., fluidic pressure in the extensionchamber may be 5 Pa larger than fluidic pressure in the compressionchamber); alternatively, when an applied torque of −10 N·m is applied tothe pump, a pressure differential of −5 Pa is generated (e.g., fluidicpressure in the extension chamber may be 5 Pa less than fluidic pressurein the compression chamber) by the pump. It is noted that this signconvention of the applied torque may be reversed.

The sign convention and the exemplary values discussed above areexemplary and are selected for illustrative purposes as the disclosureis not so limited.

As described above, the pressure differential ΔP_(pump) may be +5 Pa foran applied torque of +10 N·m. The inventors have recognized that it ispossible to control the distribution of this differential pressureacross the piston by controlling the relative stiffness of the system onthe compression volume side relative to the stiffness on the extensionvolume side. The inventors have further recognized that by controllingthis distribution, it is possible to achieve a range of forces on thepiston for the same deferential pressure produced by the pump orhydraulic motor. The inventors have therefore realized that, byadjusting the stiffness and/or compliance of the compression-side of theactuator relative to the stiffness and/or compliance of theextension-side of the actuator (e.g., by adding one or moreaccumulators), it is possible to influence how fluidic pressure in thecompression chamber and/or extension chamber responds to a torqueapplied to the pump.

For example, if the system in FIG. 3 is effectively symmetric (e.g., astiffness of the compression chamber and compression side flow path iseffectively equal to a stiffness of the extension chamber and extensionside flow path), then a fluidic differential pressure produced by thepump would be divided equally between the compression and extensionsides of the system. In the example described above where thedifferential pressure produced by the pump was +5 Pa, pressure of theextension chamber (denoted Pext in equation 1) would increase to +2.5 Paabove the static pressure or precharge pressure (i.e., the fluidicpressure of the system under static conditions at a time at which notorque may be applied to the pump, denoted Pstatic); likewise, a fluidicpressure of the compression chamber (denoted Pcom in equation 1) woulddecrease to −2.5 Pa below the static or precharge pressure. As a result,the pressure differential, ΔP_(pump), given by equation 1 is:Pext−Pcom=(P_(static)+2.5 Pa)−(P_(static)−2.5 Pa)=+5 Pa.

In a non-symmetric system, where the stiffness or compliance of thecompression-side of the actuator is not effectively equal to thestiffness or compliance of the extension-side of the actuator, thepressure distribution would be different. For example, as illustrated inFIG. 1, a single accumulator may be utilized located on thecompression-side of the actuator. In this case the gas volume of thecompression-side accumulator is large such that the compression-side ofthe actuator (which includes the compression chamber, thecompression-side flow path, and, if present, the compression-sideaccumulator) may be significantly softer than the extension-side of theactuator (which includes the extension chamber, the extension-side flowpath, and, if present, the extension-side accumulator).

Similar to the discussion about the hydraulic system of FIG. 3 discussedabove, if an applied torque of 10 N·m is applied to a pump of FIG. 1with an exemplary displacement of 2 cubic meters, a pressuredifferential ΔP_(pump) of +5 Pa may be generated by the pump. However,in the case of the hydraulic system of FIG. 1, the fluidic pressure ofthe compression chamber will remain effectively constant at the staticor precharge pressure (that is, Pcom=Pstatic), while the fluidicpressure of the extension chamber may increase to +5 Pa relative to thestatic or precharge pressure (that is, Pext=Pstatic+5 Pa). This behaviorwould be due to the softness of the compression-side of the actuatorrelative to the extension-side of the actuator. The overall ΔP_(pump) asdetermined by equation 1 is: Pext−Pcom=(P_(static)+5 Pa)−(P_(static))=+5Pa.

Thus, in the above example, while the pressure differential, ΔP_(pump),generated by the pump may be unaffected by addition of thecompression-side accumulator (in each case it is +5 Pa), the magnitudeof variation of fluidic pressure in the compression chamber (ΔP_(com))is substantially affected, as is the magnitude of the variation offluidic pressure in the extension chamber (P_(ext)). Mathematically, thevariation in fluidic pressure of the extension chamber (denotedΔP_(ext)) as compared to the static or precharge pressure (Pstatic) is afunction of the compliance of the extension-side of the circuit (denotedCext), the compliance of the compression-side of the circuit (denotedCcom), and the pressure differential generated by the pump (ΔP_(pump))as determined by equation 4. Likewise, the variation in fluidic pressureof the compression chamber (denoted ΔP_(com)) may be determined byequation 5.

$\begin{matrix}{{\Delta P_{ext}} = {{{Pext} - {Pstatic}} = {{\frac{Ccom}{{Cext} + {Ccom}}\Delta P_{pump}} = {\left( {1 - \frac{Cext}{{Cext} + {Ccom}}} \right)\Delta P_{pump}}}}} & {{Equation}\mspace{14mu} 4} \\{\mspace{79mu}{{\Delta\; P_{com}} = {{{Pcom} - {Pstatic}} = {\frac{{- C}ext}{{Cext} + {Ccom}}\Delta P_{pump}}}}} & {{Equation}\mspace{14mu} 5} \\{\mspace{79mu}{{\Delta\; P_{pump}} = {{{Pext} - {Pcom}} = {{\Delta P_{ext}} - {\Delta P_{com}}}}}} & {{Equation}\mspace{14mu} 6}\end{matrix}$

As indicated by the above equations, if the system is symmetric(Cext=Ccom), then the magnitude of variation of fluidic pressure of theextension chamber (ΔP_(ext)) is effectively equal to the magnitude ofvariation of fluidic pressure of the compression chamber (ΔP_(com)). Ifthe compression-side of the circuit is significantly softer than theextension-side of the actuator (that is, Ccom>>Cext), then variations influidic pressure of the extension chamber would account for effectivelythe entire generated pressure differential (that is,ΔP_(ext)≈ΔP_(pump)). If, on the other hand, the extension-side of theactuator is much softer than the compression-side of the circuit, thenvariations in fluidic pressure of the compression chamber would accountfor nearly the entire generated pressure differential. Equations 4-6 canbe rewritten in terms of respective stiffness values (i.e. thereciprocal of compliance) instead of compliance values.

In the embodiment illustrated in FIG. 3, which includes both anextension-side accumulator 62 and a compression-side accumulator 52. afirst torque may be applied to the pump such that the pump to generatesa pressure differential of +100 psi, and wherein the static or precharge(or resting) pressure of the system is 500 psi. Therefore, wheneffectively no torque is applied to the pump, the fluidic pressure inboth the extension chamber (Pext) and the compression chamber (Pcom)would be 500 psi. When the first torque is applied to the pump, apressure differential of +100 psi is generated across the pump (i.e. thefluidic pressure of the extension chamber would exceed that of thecompression chamber by 100 psi). Such pressure differential can beaccomplished a variety of ways, such as, for example:

-   -   [a] fluidic pressure of the extension chamber may be increased        to 600 psi, while the fluidic pressure of the compression        chamber remains effectively constant at 500 psi;    -   [b] fluidic pressure of the extension chamber may be increased        to 550 psi, while the fluidic pressure of the compression        chamber is decreased to 450 psi; or    -   [c] fluidic pressure of the extension chamber may remain        constant at 500 psi, while the fluidic pressure of the        compression chamber is decreased to 400 psi.

As should be evident from the analysis above, case [a] may occur whenthe compression-side of the circuit is much softer (lower stiffnessand/or higher compliance) than the extension-side of the circuit; case[b] may occur when the system is symmetric; and case [c] may occur whenthe extension-side of the circuit is significantly softer than thecompression-side of the circuit. Any of these exemplary cases [a]-[c]may be induced as a result of the same pressure differential of +100psi. Inventors have realized that these different distributions resultin different forces being applied to the piston.

The force transmitted to the piston along a direction parallel to thelongitudinal axis of the piston rod (denoted F) is given by equation 7or 8 below, where P_(ext) is the fluidic pressure in the extensionchamber, P_(com) is the fluidic pressure in the compression chamber,A_(ext) is the area of the face of the piston that is exposed to fluidpressure in the extension chamber that results in a force in thelongitudinal direction, A_(com) is the area of the face of the pistonthat is exposed to fluid pressures in the compression chamber thatresults in a force in the longitudinal direction, andΔA=A_(com)−A_(ext).

F=P _(ext) *A _(ext) −P _(com) *A _(com)  Equation 7

F=P _(ext)*(A _(com) −ΔA)−P _(com) *A _(com)  Equation 8

Assuming the piston and piston rod both possess a circularcross-sectional area, the values A_(ext), A_(com), and ΔA can be relatedto the diameter of the piston (Dpiston) and diameter of the piston rod(Drod) using equations 9-11 below.

A _(com)=pi*(Dpiston/2)²  Equation 9

A _(ext)=pi*(Dpiston/2)²−pi*(Drod/2)²  Equation 10

ΔA=A _(rod)=pi*(Drod/2)²  Equation 11

For an embodiment where the diameter of the piston is 10 inches,yielding an Acom value of 25*pi square inches. If the diameter of thepiston rod is 2 inches Aext would equal 24*pi square inches. Thedimensions of the embodiment are exemplary as the disclosure is not solimited, and indeed the discussion would be applicable for anyappropriate piston and rod combination.

Considering case [a] above (Pext=600 psi, Pcom=500 psi) and utilizingequation 4, a force having a magnitude of 1900*pi pounds is transmittedto the piston in response to the 100 psi pressure differential generatedby the pump. For case [b] above (Pext=550 psi, Pcom=450 psi), a forcehaving a magnitude of 1950*pi pounds is transmitted to the piston inresponse to the +100 psi pressure differential generated by the pump.For case [c] above (Pext=500 psi, Pcom=400 psi), a force having amagnitude of 2000*pi pounds is transmitted to the piston in response tothe +100 psi pressure differential generated by the pump.

As is evident from the above discussion, the same applied torque and thesame generated pressure differential ΔP_(pump) by the pump may result indifferent forces being transmitted to the pump depending on the relativestiffnesses or compliances of the compression side of the circuitrelative to the extension side of the circuit. Combining equations 2-11,the force transmitted to the piston (F) may be related to a generatedpressure differential (ΔP_(pump)) by equation 12.

$\begin{matrix}{F = {{\Delta{P_{pump}\left( {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta A}} \right)}} + K}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

Substituting for ΔP_(pump) using equation 3 allows the force transmittedto the piston to be further related to the applied torque and thedisplacement of the pump.

$\begin{matrix}{F = {{\frac{\tau_{applied}}{Disp}\left\lbrack {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta A}} \right\rbrack} + K}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

Equation 13 may be rearranged in order to yield a ratio (F/τ_(applied))between the force transmitted to a piston and a torque applied to thepump, as shown in equation 14. This ratio may be referred to as a motionratio of the actuator, denoted R_(motion).

$\begin{matrix}{{R_{motion} \propto \frac{F}{\tau_{applied}}} = {\frac{1}{Disp}\left\lbrack {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta A}} \right\rbrack}} & {{Equation}\mspace{14mu} 14}\end{matrix}$

Equation 14 was derived from equations 1-13, assuming no mechanicalloss, hydraulic loss, drag, or inertia; as would be recognized by one ofordinary skill, however, additional factors, including, for example,those shown in equation 2, may be incorporated into equation 13. Theterm “K” in equation 13 used to account for any static forces that areplaced on the rod as a result of internal static pressure on the rodarea.

As shown in equation 15, the motion ratio (R_(motion)) may alternativelybe expressed in units of angular rotation of the pump (e.g., in units ofradians) to linear displacement of the piston (e.g., in units ofmeters). In this light, the motion ratio (R_(motion)) may be thought ofas relating the angular displacement of the pump (denoted θ) to lineardisplacement of the piston (denoted D), higher motion ratios indicatemore rotation of the pump in response to a given linear motion of thepiston.

$\begin{matrix}{{R_{motion} \propto \frac{\theta}{D}} = {\frac{1}{Disp}\left\lbrack {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta A}} \right\rbrack}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

The steady state active force produced by the system can, therefore, bedetermined by the applied torque multiplied by the motion ratio. As canbe seen from equation 14, in order to maximize the force transferred inresponse to a given applied torque, it may be desirable in certainembodiments for the extension-side of the circuit to be softer than thecompression-side of the circuit (leading to a higher motion ratio). Thiscan be accomplished, for example, by placing an accumulator only on theextension-side of the circuit (e.g., along the extension-side flow path)and not on the compression-side of the circuit; or by using both anextension-side accumulator and a compression-side accumulator, whereinthe extension-side accumulator is much larger (e.g., has a larger gasvolume) or softer than the accumulator on the compression-side of thecircuit.

In automotive applications, it is contemplated that a hydraulicactuator, such as, for example, those illustrated herein, may beutilized to minimize oscillating motions (e.g., vibrations) of one ormore components of the vehicle.

An oscillating applied torque may be specified by both a frequency ofthe oscillations, and by an amplitude of the oscillations. For example,a first torque of +10 N·m may be applied to the pump for 0.5 s,immediately after which a second torque of −10 N·m may be applied to thepump for 0.5 s. This cycle may be repeated any number of times, yieldinga periodic applied torque profile. Such periodic applied torque profilehas a frequency of 1 Hz (1 full cycle per second) and an amplitude of 10N·m. Alternatively, instead of periodic step input, the input mayoscillate according to a sinusoidal wave, or according to any otherregular or irregular waveform.

In case of an oscillating applied torque, equation 3 may be modified toexpress the generated pressure differential as a function of time:

$\begin{matrix}{{\Delta{P_{pump}(t)}} = \frac{\tau_{applied}(t)}{Disp}} & {{Equation}\mspace{14mu} 15a}\end{matrix}$

Given a periodically oscillating applied torque, the pressuredifferential ΔP_(pump) generated by the pump may periodically vary withtime. In the case of an exemplary displacement value of 2 cubic meters,when an torque of +10 N·m is applied to the pump, a pressuredifferential (ΔPpump) of +5 Pa is generated (e.g., fluidic pressure inthe extension chamber is 5 Pa larger than fluidic pressure in thecompression chamber), while when a torque of −10 N·m is applied to thepump, a pressure differential (ΔPpump) of −5 Pa is generated (e.g.,fluidic pressure in the extension chamber is 5 Pa less than fluidicpressure in the compression chamber). It is noted that this signconvention is arbitrary, and may be reversed without affecting thefundamental analysis herein.

Continuing with the above exemplary case, as the applied torqueoscillates between +10 N·m and −10 N·m, the resulting pressuredifferential ΔP_(pump)(t) generated by the pump correspondinglyoscillates between +5 Pa and −5 Pa. The amplitude of this exemplaryoscillating pressure differential, ΔP_(pump)(t), is therefore 5 Pa, andthe peak-to-peak amplitude is 10 Pa. For the purposes of thisdisclosure, the amplitude of any oscillating value, v(t), may beexpressed using the nomenclature Â{v(t)}. For example, the amplitude ofan oscillating pressure differential may be represented asÂ{ΔP_(pump)(t)}, and may be related to the amplitude of the oscillatingapplied torque by equation 15b.

$\begin{matrix}{{\overset{\hat{}}{A}\left\{ {\Delta{P_{pump}(t)}} \right\}} = \frac{\overset{\hat{}}{A}\left\{ {\tau_{applied}(t)} \right\}}{Disp}} & {{Equation}\mspace{14mu} 15b}\end{matrix}$

It is noted that, as with equation 3, equations 15a-b assume anefficiency value of 1 and neglects drag torque and inertial effects.Equations 15a-b may be modified by one of ordinary skill in the art toaccount for such additional factors.

An oscillating pressure differential ΔP_(pump)(t) causes oscillations inthe fluidic pressure of the extension chamber relative to the static orprecharge pressure (ΔPext(t)), and/or in the fluidic pressure of thecompression chamber relative to the static or precharge pressure(ΔPcom(t)). The amplitude of Pext(t) and ΔPext(t) may be represented byequation 16, while the amplitude of Pcom(t) and ΔPcom(t) may berepresented by equation 17.

$\begin{matrix}{{\hat{A}\left\{ {\Delta{P_{ext}(t)}} \right\}} = {{\hat{A}\left\{ {P_{ext}(t)} \right\}} = {\left( {1 - \frac{Cext}{{Cext} + {Ccom}}} \right)*\hat{A}\left\{ {\Delta{P_{pump}(t)}} \right\}}}} & {{Equation}\mspace{14mu} 16} \\{{\hat{A}\left\{ {\Delta{P_{com}(t)}} \right\}} = {{\hat{A}\left\{ {P_{com}(t)} \right\}} = {\frac{Cext}{{Cext} + {Ccom}}*\hat{A}\left\{ {\Delta{P_{pump}(t)}} \right\}}}} & {{Equation}\mspace{14mu} 17}\end{matrix}$

As can be seen by examination of equation 16-17, if the system issymmetric (C_(com)=C_(ext)), then the amplitude of ΔPext(t) and ΔPcom(t)are theoretically equal. If the compression-side of the circuit is muchsofter than the expression side of the circuit (C_(com)>>C_(ext)), thenthe amplitude of ΔP_(com)(t) is lower than that of ΔP_(ext)(t) (that is,the fluidic pressure of the compression chamber remains relativelyconstant compared to that of the extension chamber).

These oscillations in fluidic pressures of the extension chamber and/orcompression chamber may thereby cause the force transmitted to thepiston to oscillate. In the case of oscillating torques, pressures,and/or force, the motion ratio may be expressed as a ratio of theamplitude of F(t) (the force transmitted to the piston) over theamplitude of the applied torque, as shown in Equation 18. Alternatively,the motion ratio in response to oscillating input (denoted Řmotion forclarity) may be expressed as a ratio of the amplitude of angulardisplacement of the pump (e.g., in units of radians) over the amplitudeof linear displacement of the piston (e.g., in units of meters), asshown by equation 19.

$\begin{matrix}{{\overset{ˇ}{R}}_{motion} = {\frac{\overset{\hat{}}{A}\left\{ {F(t)} \right\}}{\overset{\hat{}}{A}\left\{ {\tau_{applied}(t)} \right\}} = {\frac{1}{Disp}\left\lbrack {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta\; A}} \right\rbrack}}} & {{Equation}\mspace{20mu} 18} \\{\mspace{79mu}{{\overset{ˇ}{R}}_{motion} = {\frac{\overset{\hat{}}{A}\left\{ {\theta(t)} \right\}}{\overset{\hat{}}{A}\left\{ {D(t)} \right\}} = {\frac{1}{Disp}\left\lbrack {A_{ext} + {\frac{C_{ext}}{C_{ext} + C_{com}}\Delta A}} \right\rbrack}}}} & {{Equation}\mspace{14mu} 19}\end{matrix}$

Analogous to the discussion of equation 14, it can be seen that themotion ratio (and therefore force capability for a given applied torque)may be increased by increasing the compliance of the extension-side ofthe circuit relative to the compression-side of the circuit.

The inventors have recognized that, especially for automotive suspensionapplications, it may be advantageous to design a hydraulic system havingan increased force capability and motion ratio for low speed events(e.g., low-frequency oscillating motions), while having decreased motionratio and force capability—but faster response time—for high speedevents (e.g., high-frequency oscillating motion). Low frequency motionmay be associated with control of a vehicle body (‘body control’), andmay occur, for example, when lifting up or lowering a vehicle in orderto traverse a large pothole or large bump. For low speed events orlow-frequency oscillating motion, it may be desirable to have high forcecapability in order to achieve the desired control over accelerations ofthe vehicle body relative to one or more wheels of the vehicle. Asdiscussed above, force capability may be increased by increasing themotion ratio, e.g. by increasing the compliance of the extension-side ofthe circuit relative to the compliance of the compression-side of thecircuit.

Increasing the compliance of the extension-side of the circuit also actsto slow the response time of the actuator. A given response time may benegligible compared to the duration of a low speed event (or period of alow-frequency oscillation), but may become significant compared to theduration of a high speed event (or period of high frequencyoscillation). For example, a response time of 0.05 s may be negligiblefor a low-speed event having a duration of 1 s. However, the same 0.05 sresponse time is significant for an event having a duration of 0.1 s.Therefore, for high speed events or high frequency oscillations,response time and bandwidth become a greater concern than forcecapability, and it may be advantageous to sacrifice force capability inreturn for improved response time. This may be done by, for example,decreasing the relative compliance of the extension-side of theactuator, leading to a decreased motion ratio. Additionally, decreasingthe motion ratio of the actuator for high speed events may also act tominimize the transmission of high speed wheel inputs from the wheel tothe vehicle body. Additionally or alternatively, reducing the motionratio for high speed events may help to reduce the inertia effects ofthe pump on the vehicle suspension system.

In light of the above analyses, the inventors have realized that it maybe advantageous to design a hydraulic actuator in which the motion ratioof the actuator may be dynamically varied. This may be accomplished bydynamically varying the stiffness and/or compliance of theextension-side of the actuator and/or the stiffness and/or compliance ofthe compression-side of the actuator. For example, for low frequencyoscillations in pressures, it may be desirable to increase thecompliance of the extension-side of the circuit relative to thecompression-side of the circuit, thereby maximizing motion ratio andforce capability for a given torque. For high frequency oscillations, itmay be desirable to decrease the compliance of the extension-side of theactuator relative to the compression-side of the actuator, therebyspeeding up the response time of the system at the expense of forcecapability.

FIG. 4 illustrates an exemplary corner of a suspension system includinga hydraulic actuator 64 having a dynamically variable motion ratio. Theactuator 64 of the exemplary embodiment illustrated in FIG. 4 includes apump 63, a compression-side accumulator 66, and an extension-sideaccumulator 62. The hydraulic actuator 64 further includes a restrictionelement 61 fluidically disposed between the pump 63 and theextension-side accumulator 62. In certain embodiments, the restrictionelement 61 may include one or more of a restriction, a passive valve, ashim stack, and an actively controlled valve. An actively controlledvalve may be, for example, an electrically controlled valve, ahydraulically controlled valve, or a pneumatically controlled valve.

In some embodiments the restriction element 61 may be a valve. When thevalve is open, the extension-side of the circuit may have a firstcompliance (also a first stiffness). When this valve is closed, theextension-side of the circuit may have a second compliance that may beless than the first compliance and/or a second stiffness greater thanthe first stiffness (that is, the extension-side of the circuit becomesstiffer upon closing the valve). In certain embodiments, this valve maybe an electrically or electromechanically actuated valve (e.g. asolenoid valve, a servo valve). In certain embodiments, a controller maybe configured to at least partially open the valve when the frequency ofoscillating motion of the pump (e.g., oscillating rotary motion),oscillating motion of the piston (e.g., oscillating linear motion),and/or oscillations in fluidic pressure in any part of the actuator isbelow a first threshold frequency. Likewise, the controller may beconfigured to at least partially close the valve when the frequency ofoscillating motion of the pump, oscillating motion of the piston, and/oroscillations in fluidic pressure in any part of the actuator is above asecond threshold frequency.

In certain embodiments, a vehicle may have a suspension system thatincludes a hydraulic actuator according to any embodiment disclosedherein. Additionally, the vehicle may include one or more “look ahead”sensors, such as a camera, a LIDAR system, a RADAR system, etc. The lookahead sensor may be configured to collect information about the groundsurface ahead of the vehicle. A set of one or more controllers may beconfigured to receive information from the one or more look aheadsensors, and to determine a characteristic (e.g., a frequency, a peakfrequency, a power spectral density) of an expected input based on thereceived information. For example, a certain road feature may be knownto result in a certain input having a certain characteristic. In certainembodiments, the set of controllers may be further configured to adjustthe restriction element (e.g., at least partially open a valve, at leastpartially close a valve) based on the characteristic (e.g., a frequency)of the expected input.

Alternatively, the restriction element 61 may be or may include, forexample, an orifice or a restriction that is tuned such that theextension-side accumulator effectively “cuts off” for pressureoscillations above a threshold frequency. For low frequency inputs, theflow restriction may allow fluid flow in and out of the extension-sideaccumulator 62 with minimal interference, leading to the extension-sideof the actuator having a relatively high compliance (e.g., a relativelyhigh C_(ext) value) and, therefore, a higher motion ratio. However, athigher frequency inputs above the threshold frequency (e.g., above thecutoff frequency of the flow restriction), the extension-sideaccumulator is essentially cut-off from the rest of the actuator.Therefore, only a minimal amount of fluid flow may pass into theextension-side accumulator since it is choked by the restriction. Thisreduces the effective motion ratio of the actuator by decreasing thecompliance of the extension-side of the actuator relative to thecompliance of the compression-side of the actuator (e.g., by decreasingC_(ext) relative to C_(com)). For reasons discussed previously, if theactuator 64 is used as an active suspension system, improved ridecomfort may achieved in the presence of high frequency road inputs dueto the decreased motion ratio, thereby minimizing the amount of energytransferred into a vehicle body 60. The reduced motion ratio may alsohelp to reduce the inertia effects of the pump on the vehicle suspensionsystem.

Alternatively, the restriction element 61 may be, for example, a shimstack. Due to the pressure response of a shim stack, when the rate offluidic pressure change in the extension-side of the actuator issufficiently fast, the shim stack may remain closed or effectivelyclosed. When the rate of fluidic pressure change in the extension-sideof the actuator is sufficiently slow, the shim stack may at leastpartially open, thereby increasing compliance and decreasing stiffnessof the extension-side of the actuator.

The restriction element may be tuned by, for example, utilizingcomputational fluid dynamic simulations to identify desired inertanceand/or impedance characteristics of the restriction element based ondesired frequency response, and subsequently designing the restrictionelement to match the desired inertance and/or impedance characteristicsaccording to known methods in the art. Alternatively or additionally,for initial evaluation, an adjustable valve (such as, for example, aneedle valve) may be utilized and adjusted until the desired frequencyresponse is obtained. Once the desired frequency response is obtained,the properties of the needle valve that yield the desired response maybe evaluated, and the restriction element may be designed or tuned tohave similar properties.

FIG. 5 illustrates the response of an actuator having a frequencydependent motion ratio (such as the embodiment illustrated in FIG. 4) tooscillating inputs of different frequencies. For the actuator evaluatedto produce FIG. 5, the size of the extension-side accumulator 62 isapproximately equal to the size of the compression-side accumulator 66.For oscillating inputs of a low frequency (e.g., 2 Hz), the restrictionelement 61 allows fluid to freely flow to and from the extension-sideaccumulator, resulting in approximately equal compliance in thecompression-side and the extension-side of the actuator (that is,Cext≈Ccom). Since Cext≈Ccom at 2 Hz the amplitude of oscillations ofextension chamber pressure 70 Pext(t) and compression chamber pressure71 Pcom(t) are approximately equal (as suggested by equations 16-17above). As the frequency of oscillations increase, the restrictionelement 61 progressively begins to restrict flow to and from theextension-side accumulator. Therefore, for oscillating inputs at a highfrequency (e.g. 12 Hz), the extension-side accumulator is at leastpartially choked off from the rest of the actuator, leading to adecrease in compliance of the extension-side of the accumulator (inother words, at high frequencies, Ccom>Cext). Since Ccom>Cext for inputsof a sufficiently high frequency (e.g., 12 Hz), the amplitude ofoscillations of Pcom(t) are less than the amplitude of oscillations ofPext(t) (as suggested by equations 16-17 above).

In certain embodiments, actuator behavior may be managed further byutilizing a second extension-side accumulator 75 and a secondrestriction element 76, as shown in FIG. 6. This second restrictionelement may include one or more of a valve (e.g., a spool valve, anelectrically or electromechanically actuated valve, a variablerestriction or orifice, or any other type of appropriate valve), a shimstack, or a static restriction or orifice. The principle of operation ofthe second extension-side accumulator is similar to that described abovewhen the second restriction element allows fluid to freely pass to thesecond extension-side accumulator, the compliance of the extension-sideis higher than when the second restriction element blocks or impedesfluid flow to the second-extension side accumulator. The first hydraulicdevice and second hydraulic device may be tuned to have differentthresholds or cut-off frequencies, so that three stage control ispossible.

As shown in equations 16-19, the amplitude of pressure oscillations inthe extension chamber and compression chamber, and the motion ratio, alldepend on the factor

$\frac{C_{ext}}{C_{ext} + C_{com}}.$

This factor describes a ratio of compliance of the extension-side of theactuator over the total compliance of the actuator (i.e., the sum of thecompliance of the extension-side of the actuator and the compressionside of the actuator). For clarity, this factor will be referred to asthe “relative compliance factor” and will be denoted Č.

As is evident from the above discussion, in one aspect of thisdisclosure, the inventors aim to describe the design and benefits of ahydraulic actuator having a relative compliance factor Č thatdynamically varies based on, for example, the frequency of anoscillating input or another property (such as, e.g., the speed orduration) of an input. In theory, consideration of the relativecompliance factor is quite useful for derivations of relevant equations;however, in practice, when presented with a hydraulic actuator, therelative compliance factor may be quite difficult or complex todetermine. The inventors therefore introduce a related factor referredto as the “relative pressure factor,” denoted

, that is defined by equation 20.

$\begin{matrix}{p = {\frac{\overset{\hat{}}{A}\left\{ {\Delta{P_{ext}(t)}} \right\}}{\overset{\hat{}}{A}\left\{ {\Delta{P_{com}(t)}} \right\}} = \frac{\overset{\hat{}}{A}\left\{ {P_{ext}(t)} \right\}}{\overset{\hat{}}{A}\left\{ {P_{com}(t)} \right\}}}} & {{Equation}\mspace{20mu} 20}\end{matrix}$

As shown, the relative pressure factor

represents the ratio of the amplitude of oscillations in fluidicpressure of the extension chamber over the amplitude of oscillations influidic pressure of the compression chamber in response to anoscillating input. In cases in which the pressure of the extensionchamber (Pext) and/or the pressure of the compression chamber (Pcom)oscillates in an irregular fashion (i.e., according to an irregularwaveform) in response to a given oscillating input, it is understoodthat the term “amplitude” as used herein refers to the root mean square(RMS) amplitude of the oscillations in respective pressure.

Based on the above equations, it can be shown that the relative pressurefactor

may be mathematically related to the relative compliance factor Č byequation 21.

=Č ⁻¹−1  Equation 21

The below table depicts values for the relative compliance factor C andthe relative pressure factor

for various configurations of a hydraulic actuator. As can be seen, whenthe system is symmetric (the compliance of the extension-side equals thecompliance of the compression-side, or Cext=Ccom), the relativecompliance factor Č is 0.5 and the relative pressure factor

is 1. When the extension-side is softer than the compliance-side(Cext>Ccom), the relative compliance factor Č is greater than 0.5, andthe relative pressure factor

is less than 1. When the compression-side is softer than theextension-side (Ccom>Cext), the relative compliance factor Č is lessthan 0.5, and the relative pressure factor

is greater than 1.

C_(ext) = C_(com) C_(ext) > C_(com) C_(ext) < C_(com) Relativecompliance factor {hacek over (C)} 0.5 >0.5 <0.5 Relative pressurefactor p 1 <1 >1 Notes higher motion lower motion ratio and ratio andforce output force output

As shown, the force capability of the system (and motion ratio) isinversely proportional to the relative pressure factor: that is, lowerrelative pressure factors lead to higher force capability and motionratios and higher relative pressure factors lead to lower forcecapability and motion ratios. As evident from the above discussion ofdynamically controlled hydraulic actuators, preferably an actuator willexhibit a first relative pressure factor for oscillating inputs of afrequency below a first threshold, and a second relative pressure factorthat is higher than the first relative pressure factor for oscillatinginputs of a frequency above a second threshold, wherein the secondthreshold is equal to or greater than the first threshold. In certainembodiments, the first threshold may be below a wheel-hop frequency of avehicle and the second threshold may be above the wheel-hop frequency ofthe vehicle. In certain embodiments, the first and second threshold mayfall within the range of 3 Hz-7 Hz. Preferably, the first relativepressure factor is 1 or less than 1, and/or the second relative pressurefactor is greater than 1.

For example, returning to FIG. 5, for inputs of low frequencies (e.g., 2Hz, e.g., below the cutoff frequency of the restriction element 61), theevaluated actuator exhibits a relative pressure factor

of approximately 1. However, as the frequency of the input increases,the relative pressure factor

can be seen to increase, such that at high frequencies (e.g., 8 Hz, 10Hz, 12 Hz) the relative pressure factor

is greater than 1.

Therefore, the preferred properties of the actuator may be defined interms of, for example, a relative compliance factor or a relativepressure factor. However, as noted above, in practice it may be easierto determine the relative pressure factor of a given actuator as opposedto the relative compliance factor of the actuator.

The relative pressure factor of a given actuator in response to anoscillating input of a given frequency may be determined as follows. Afirst pressure sensor may be placed in the extension chamber of theactuator, and a second pressure sensor may be placed in the compressionchamber of the actuator. The piston rod may be held in place (e.g.,using a dynamometer) with the piston located at approximatelymid-stroke. With the piston rod held in place, an oscillating torque ofa first frequency may be applied to the pump (e.g., to the shaft of thepump), thereby causing the fluidic pressure in the extension chamber tooscillate and/or the fluidic pressure in the compression chamber tooscillate. The amplitude of oscillations of fluidic pressure in theextension chamber and the amplitude of oscillations of fluidic pressurein the compression chamber may be determined using the first pressuresensor and second pressure sensor, respectively. The ratio of theseamplitudes then gives the relative pressure factor. In order todetermine a frequency dependence of the relative pressure factor, thetest may be repeated using an oscillating torque of a differentfrequency and the same amplitude.

Alternatively, the relative pressure factor of a given actuator inresponse to an oscillating input of a given frequency may be determinedby locking the pump in place (e.g., by preventing rotation of the pump'sshaft) and oscillating the position of the piston (e.g., by applying anoscillating force to an end of the piston rod, thereby causing thepiston to move up and down relative to the housing of the hydrauliccylinder). For example, the actuator may be placed in a dynamometer andthe piston may be moved to approximately mid-stroke. A brake or othermechanical device may be used to lock the pump in place, so that itcannot rotate. The position of the piston may be oscillated according toa first frequency, thereby causing the fluidic pressure of the extensionchamber to oscillate and/or the fluidic pressure of the compressionchamber to oscillate. The amplitude of oscillations of fluidic pressurein the extension chamber and the amplitude of oscillations of fluidicpressure in the compression chamber may be determined using the firstpressure sensor and second pressure sensor, respectively. The ratio ofthese amplitudes determines the relative pressure factor. In order todetermine a frequency dependence of the relative pressure factor, thetest may be repeated using an oscillating linear displacement of adifferent frequency, or a range of frequencies, and the same amplitude.

For the above described methodologies, the input (that is, the torqueapplied to the pump or the position of the piston) may be oscillatedaccording to a regular wave (e.g., a pure sinusoidal wave), or the inputmay be oscillated according to any other regular or irregular waveform.For example, the oscillating input may oscillate according to asinusoidal wave superimposed on a constant offset, or a sinusoidal wavesuperimposed on an offset that increases linearly with time. In the caseof an oscillating input that oscillates according to an irregularwaveform, it is recognized that the “frequency” of such input, as usedherein, may refer to the peak frequency, and the “amplitude” of suchinput, as used herein, may refer to the root mean square (RMS)amplitude.

The cutoff frequency of the restriction element 61 may be adjusted basedon, for example, the specific requirements of a given application. Foran active suspension system of a road vehicle, this cutoff frequency maybe selected to be, for example, between 3 and 10 Hz. Other cut-offfrequencies both above and below this range may also be selected as thedisclosure is not so limited.

In some embodiments, below the cut-off frequency, the extension-side ofthe actuator may have a first compliance that leads to first motionratio of the actuator. Above this cutoff frequency, the extension-sideof the actuator may have a second compliance that is less than the firstcompliance; correspondingly, for oscillations above the cutofffrequency, the actuator may have a second motion ratio that is less thanthe first motion ratio. Such design may allow for maximizing forcecapability in order to oppose motion at typical vehicle heave, pitch,and roll frequencies, while mitigating the transmission of impacts intothe vehicle body 60 above these frequencies. Typically, motion of thevehicle body in heave, pitch and/or roll (e.g. primary ride) occurs atfrequencies that are lower than road induced secondary ride frequencies.

Table II describes an exemplary implementation of the embodiment shownin FIG. 6, but other configurations or arrangements of this embodimentmay be configured, and the disclosure is not so limited.

TABLE II Piston rod diameter  18 mm Piston Diameter  46 mm Compressionchamber accumulator gas volume 125 cc Extension chamber accumulator gasvolume 160 cc System static charge pressure  35 bar Pump Displacement3.19e−7 m{circumflex over ( )}3/rad Pump rotational inertia  2.3e−5 kg *m{circumflex over ( )}2

Table III below describes exemplary performance of an embodiment of FIG.4 that is sized according to Table II. The hydraulic stiffness of thecompression and extension chambers during operation may be at leastpartly a function of the pressure change in each chamber as a result offluid flow through the pump. In this embodiment, the accumulators may becharged with a pressurized gas but in other embodiments the accumulatorsinclude springs (e.g., linear springs, non-linear springs). Thenon-linear stiffness associated with the compression and expansion ofgas in accumulators plays a roll in determining the difference betweenforces produced in the positive direction and those that are produced inthe negative direction.

TABLE III Low Frequency System High Frequency System Performance (belowPerformance (above Improvement cutoff frequency of 3 Hz) cutofffrequency of 3 Hz) Force Reflected Pump Delta Motion Force ReflectedMotion Force Reflected Reduction mass reduction Pressure Ratio Outputpump mass Ratio Output pump mass above cutoff above cutoff [bar] [rad/m][N] [kg] [rad/m] [N] [kg] frequency (%) frequency (%) −20 3447 −2340 2723142 −2100 226 10.3% 17.0% 0 3600 0 302 3142 0 226 — — 20 3806 2550 3323142 2100 226 17.7% 32.0%

FIG. 7 illustrates a graph 80 that compares the improved performancethat may be achieved at the damper by using the embodiment of FIG. 4.Curve 81 is a plot of the force that may be generated by using theembodiment of FIG. 1. In this embodiment, only a compression-sideaccumulator 30 is present, and the actuator does not contain anextension-side accumulator. The compliance of the compression-side ofthe actuator is therefore much larger than the compliance of theextension-side of the actuator (Ccom>>Cext). The curve 81 represents theforce that is produced by the actuator (on the y-axis) illustrated inFIG. 1 as a function of power input to the hydraulic pump (on thex-axis). The curve 82 represents the force produced by the actuatorshown in FIG. 4 versus the power input. In this comparison, pump 31 andpump 63 are the same pump (e.g., same mechanical efficiency, samedisplacement, etc.). This illustration is shown for steady state forcesgenerated for low frequency motion. As can be seen, addition of theextension-side accumulator leads to a higher force capability, asdiscussed previously.

In some embodiments, the behavior of motion ratio as a functionfrequency may be determined by other factors in addition to relativecompliance ratio, such as, for example various system resonances. FIG. 8illustrates the relative motion ratios the embodiments of FIG. 1. (curve92), FIG. 2 (curve 91), and FIG. 4 (curve 93). Here, the mass resonanceof the system is shown contributing to the relative motion ratio. Themotion ratio peak shown here at approximately 15 hz, is not caused bythe change in relative compliance factor, but by an undamped resonanceof the pump mass on the accumulator spring elements in the hydraulicsystem. This acts similar to a mass spring system (wherein the pumpserves as the mass and the hydraulic compliance serves as the spring).The resonance frequency may be determined by the stiffness or complianceof the hydraulic system and the inertia of the rotating mass of thehydraulic pump. Curve 93 illustrates that, at low frequencies, theembodiment in FIG. 4 produces approximately 20% more force for the sametorque input to the same hydraulic motor. The motion ratio transferfunction exhibits a reduction at approximately 2-5 Hz which is a resultof the change in the relative compliance factor as frequency increasesin a system described by FIG. 4. It is also noted that since thecompliance of the extension volume is being reduced by flow restriction,the resonance peak of the pump mass on the system compliance is reduced.In this illustration, the pump mass resonance occurs at approximately 15hz.

FIG. 9 illustrates a frequency-response plot that depicts therelationship between velocity inputs at the wheel and the forcestransmitted to the body of the vehicle for three embodiments. Curve 101represents the response of the embodiment shown in FIG. 1. At about 15Hz, there is a large impedance due to the rotating mass of the pumposcillating on the stiffness of the fluid column. The curve 102 showsthe response of the embodiment of FIG. 2. Since the embodiment describedby FIG. 2 has a higher motion ratio, there is a higher system impedanceat all frequencies and a much larger impedance at the resonance point ofabout 15 Hz. The curve 103 shows the response of the embodiment of FIG.4. The system impedance is slightly higher at frequencies belowapproximately 5 Hz, but the system resonance is greatly reduced at thesystem resonance point. By using the embodiment of FIG. 4, pump elementswith higher inertia may be used while maintaining a lower level ofimpedance within a predetermined range of frequencies.

Further, for the embodiment of FIG. 4 the delta pressure produced by thepump may be split across both the extension volume and the compressionvolume. This approach may be used to reduce the peak pressures in thesystem while exerting similar output forces. This may result in lessmechanical stress and longer lasting hydraulic sealing elements.

In certain embodiments, compliance in a given hydraulic actuator may beprovided by one or more discrete or distributed compliance elements suchas, for example, gas-charged accumulators. In certain embodiments,instead of or in addition to a gas-charged accumulator, compliance maybe provided by one or more spring loaded pistons, one or more elastichoses, and/or one or more deformable housings. In the case of a springloaded piston, the compliance element may be an accumulator with aspring loaded piston where the compliance, or a portion thereof, may bedynamically adjusted by using, for example, a pin that selectively locksthe piston in place (thereby at least partially negating the complianceof the spring). Further, in certain embodiments, compliance may beprovided primarily via compression and expansion of gas dissolved in thehydraulic fluid.

In some embodiments, as illustrated by the exemplary embodiment in FIG.10, a suspension system may include a single extension-side accumulator1001 that is fluidically connected to the extension chambers of twodifferent actuators within a suspension system. In these embodiments,the suspension system may further include a first restriction element1007 disposed along a first flow path 1009 that connects the pump 1011of a first actuator 1003 to the extension-side accumulator 1001.Additionally or alternatively, a second restriction element 1015 may bedisposed along a second flow path 1017 that connects the pump 1019 of asecond actuator 1005 to the extension-side accumulator 1001. The firstrestriction element 1007 may be configured to vary an inertance orimpedance of the first flow path 1009 or a portion thereof, and/or thesecond restriction element 1015 may be configured to vary an inertanceor impedance of the second flow path 1017 or a portion thereof. In theillustrated embodiment the extension-side compliance of the firstactuator 1003 and the extension-side compliance of the second actuator1005 may be independently controlled while requiring only a single,common extension-side accumulator 1001. Utilizing a single, commonextension-side accumulator may reduce packaging requirements. Further,systems utilizing an extension-side accumulator that is common betweenmultiple actuators, may have additional force capability as contributedby the rod area and delta pressure.

In some embodiments, a vehicle may comprise a first pair of coupledactuators, such as the first actuator and second actuator illustrated inFIG. 10, and a second pair of coupled actuators. In certain embodiments,the first pair may be located on the left side of the vehicle (in whichcase the first actuator of the first pair may correspond to the leftfront tire, and the second actuator of the first pair may correspond tothe left rear tire) and the second pair may be located on the right sideof the vehicle (in which case the first actuator of the second pair maycorrespond to the right front tire, and the second actuator of thesecond pair may correspond to the right rear tire). Alternatively, thefirst pair may be located in the front of the vehicle and the secondpair may be located in the back of a vehicle. Alternatively, the firstand second actuators of the first pair may be located in diagonallyopposite corners of the vehicle, and/or the first and second actuatorsof the second pair may be located in diagonally opposite corners of thevehicle.

What is claimed is:
 1. A hydraulic actuator comprising: a hydrauliccylinder that includes an extension chamber and a compression chamber; ahydraulic pump, with a first port and a second port, capable ofgenerating a pressure differential between the compression chamber andthe extension chamber; a hydraulic circuit including an extension-sideand a compression-side, wherein the extension-side of the circuitincludes the extension chamber and a first fluid flow path fluidicallyconnecting the first port to the extension chamber, and wherein thecompression-side of the circuit includes the compression chamber and asecond fluid flow path fluidically connecting the second port to thecompression chamber; wherein the hydraulic actuator exhibits a firstrelative compliance factor when exposed to a first oscillating input,and a second relative compliance factor when exposed to a secondoscillating input, wherein: the frequency of the first oscillating inputis less than the frequency of the second oscillating input, and thefirst relative compliance factor is greater than the second relativecompliance factor.
 2. The hydraulic actuator of claim 1, wherein theextension-side of the circuit has a first compliance that is at leastpartially determined by a first compliance element and thecompression-side of the circuit has a second compliance that is at leastpartially determined by second compliance element.
 3. The hydraulicactuator of claim 2, wherein the first compliance element is one of agas charged accumulator in fluid communication with the first fluid flowpath via an intervening restriction element, an accumulator with aspring loaded piston in fluid communication with the first fluid flowpath via an intervening restriction element, and a hydraulic hose with aflexible wall segment that forms at least a portion of the first fluidflow path; and wherein the second compliance element is one of a gascharged accumulator in fluid communication with the second fluid flowpath, an accumulator with a spring loaded piston in fluid communicationwith the second fluid flow, and a hydraulic hose with a flexible wallsegment that forms at least a portion of the first fluid flow path.
 4. Ahydraulic actuator comprising: a hydraulic cylinder that includes anextension chamber and a compression chamber; a hydraulic pump, with afirst port and a second port, capable of generating a pressuredifferential between the compression chamber the extension chamber; afirst compliance element; a second compliance element; a first fluidflow path fluidically connecting the first port to the first complianceelement; a second fluid flow path fluidically connecting the first portto the extension chamber; a third fluid flow path fluidically connectingthe second port to the second compliance element; a fourth fluid flowpath fluidically connecting the second port to the compression chamber;wherein the hydraulic actuator exhibits a first relative compliancefactor when exposed to a first oscillating input, and a second relativecompliance factor when exposed to a second oscillating input, wherein:the frequency of the first oscillating input is less than the frequencyof the second oscillating input, and the first relative compliancefactor is greater than the second relative compliance factor.
 5. Thehydraulic actuator of claim 4, wherein the first compliance element isone of a gas charged accumulator and an accumulator with a spring-loadedpiston, wherein the second compliance element is one of a gas chargedaccumulator, and an accumulator with a spring loaded piston; and whereinthe first flow path includes an intervening restriction element.
 6. Thehydraulic actuator of claim 5, wherein at least a portion of the firstflow path and a portion of the second flow path are the same flow pathand at least a portion of the third flow path and the fourth flow pathare the same flow path.
 7. The hydraulic actuator of claim 5, whereinthe frequency of the first oscillating input is between 0-3 Hz and thefrequency of the second oscillating input is between 8-20 Hz.
 8. Thehydraulic actuator of claim 5, wherein the intervening restrictionelement is at least one of poppet valve, shim stack, electricallycontrolled valve, pneumatically controlled valve and an orifice.
 9. Thehydraulic actuator of claim 4, wherein the intervening restrictionelement is configured to vary an impedance of the first flow path basedat least in part on a frequency of an input.
 10. The hydraulic actuatorof claim 4, wherein the intervening restriction element is an activevalve and wherein the hydraulic actuator further includes a controllerconfigured to actuate the active valve based at least in part on afrequency of an input.
 11. The hydraulic actuator of claim 5, whereinthe hydraulic cylinder further includes: a housing at least partiallyenclosing an internal volume containing a quantity of hydraulic fluid; apiston slidably received in the housing, thereby dividing the internalvolume into a compression chamber and an extension chamber; a piston rodattached to the piston.
 12. A hydraulic actuator comprising: a hydrauliccylinder that includes an extension chamber and a compression chamber; ahydraulic pump, with a first port and a second port, arranged togenerate a pressure differential between the compression chamber theextension chamber; a first gas charged accumulator; a second gas chargedaccumulator; a first fluid flow path fluidically connecting the firstport to the first gas charged accumulator; a second fluid flow pathfluidically connecting the first port to the extension chamber; a thirdfluid flow path fluidically connecting the second port to the second gascharged accumulator; a fourth fluid low path fluidically connecting thesecond port to the compression chamber; wherein the hydraulic actuatorexhibits a first relative pressure factor in response to a firstoscillating input, and a second relative pressure factor in response toa second oscillating input, and wherein: the frequency of the firstoscillating input is below the frequency of the second oscillatinginput; and the first relative pressure factor is less than the secondrelative pressure factor
 13. The hydraulic actuator of claim 12, whereinat least a portion of the first flow path and a portion of the secondflow path are the same flow path and at least a portion of the thirdflow path and the fourth flow path are the same flow path.
 14. Thehydraulic actuator of claim 12, wherein the frequency of the firstoscillating input is between 0-3 Hz and the frequency of the secondoscillating input is between 5-10 Hz.
 15. The hydraulic actuator ofclaim 12, further comprising a restriction element arranged along thesecond flow path.
 16. The hydraulic actuator of claim 15, wherein therestriction element is configured to vary an impedance or inertance ofthe second flow path, or a portion thereof, based at least in part on afrequency of an input.
 17. The hydraulic actuator of claim 16, whereinthe restriction element is a shim stack.
 18. The hydraulic actuator ofclaim 15, wherein the restriction element is an actively controlledvalve and wherein the hydraulic actuator further includes a controllerconfigured to actuate the valve based at least in part on a frequency ofan input.
 19. The hydraulic actuator of claim 12, wherein the hydrauliccylinder further includes: a housing at least partially enclosing aninternal volume containing a quantity of hydraulic fluid; a pistonslidably received in the housing, thereby dividing the internal volumeinto a compression chamber and an extension chamber; a piston rodattached to the piston.
 20. A hydraulic actuator comprising: a hydrauliccylinder that includes a compression chamber and an extension chamber; ahydraulic pump, with a first port and a second port, capable ofgenerating a pressure differential between the compression chamber theextension chamber; a first gas charged accumulator; a second gas chargedaccumulator; a first fluid flow path fluidically connecting the firstport to the first gas charged accumulator; a second fluid flow pathfluidically connecting the first port to the extension chamber; a thirdfluid flow path fluidically connecting the second port to the second gascharged accumulator; a fourth fluid flow path fluidically connecting thesecond port to the compression chamber; a restriction element arrangedalong the first flow path, wherein the restriction element is configuredto vary an impedance and/or inertance of the first flow path, or aportion thereof, based at least in part on a characteristic of an input.21. The hydraulic actuator of claim 20, wherein the characteristic isone of a frequency of the input, and a rate of change of the input 22.The hydraulic actuator of claim 20, wherein the restriction element isconfigured to vary the impedance of the first flow path or portionthereof based at least in part on frequency of the input.
 23. Thehydraulic actuator of claim 20, wherein the restriction element isconfigured to vary the inertance of the first flow path or portionthereof based at least in part on frequency of the input.
 24. Thehydraulic actuator of claim 20, wherein the control device includes atleast one of a passive flow restriction, a passive valve, a shim stack,and an actively controlled valve.
 25. The hydraulic actuator of claim20, wherein the control device includes at least one of a shim stack andan actively controlled valve.